A man finds that the angle of elevationof a building is 22º. After walking 20 m towards the building, he finds that the angle of elevation is 33º. Find the height of the building?

The height of the building is 21.38 m

Step-by-step explanation:

Trigonometric Ratios

The ratios of the sides of a right triangle are called trigonometric ratios.

The image attached shows the measures and angles provided in the problem. The first angle of elevation is y=22°, the man walks B=20 m and finds the new angle of elevation is x=33°.

It's required to find the height of the building H.

The tangent ratio relates the opposite side with the adjacent side of a given angle. Applying it to the larger triangle:

Multiplying by D+B:

Dividing by tan 22°

Subtracting B:

Applying to the smaller triangle:

Multiplying by D:

Substituting from [1]:

Substituting values:

Operating:

H = 21.38 m

The height of the building is 21.38 m